Are you sure this isn't an errant incidental charge and not something relating to the room/tax portion of an awards stay?
Although it might be more convenient, contacting Club Carlson to question the legitimacy of a charge at a hotel is not the quickest path to resolution. Unless there has been a radical change in policy from when I worked for Radisson, CC representatives do not have unfettered access to the property management systems of individual hotels.
Honestly, the easiest way to resolve a billing question is by talking directly to a person that can access the transaction. In this case, that's the hotel.
Also, I'm not sure that I'd consider 5 days to be that long. It takes time for someone at CC to read your complaint and send it to the hotel. Then, the hotel has to have time to research and respond. Remember, just because hotels are open 24/7 doesn't mean that all departments are always open. Accounting would traditionally be closed weekends. Once the hotel responds, it takes time for a CC representative to read and evaluate the response before they can contact you. If clarification is needed, it could take another day to get an answer.
Anyway, that's just the point-of-view from someone that worked for the brand.